Your question brought to my mind the following question. Since TS and SH are both descriptors that indicate the intensity of precipitation, can they both exist simultaneously? Sort of like when does fast become slow? Or, in the case of the weather phenomenon RA, at what point does gray become black or white instead of both? A quick google search turned up the following article from a local meteorologist.
Thunderstorm, Thundershower...What's the Difference?
March 16, 2001 at 1:51 AM EST - Updated July 1 at 10:45 AM
What's the difference between a
thundershower and a thunderstorm? That is
a question that has a technical and
psychological answer. Technically, any
cloud producing lightning is considered a
thunderstorm, even if there is no rain
falling. The National Weather Service
reports it as "TS" in their hourly
observations at the airport. TSRA means a
Thunderstorm with a Rain Shower, which is
what most of us think of when we think of
thunderstorms...Thunder, Lightning and
Rain. But, when meteorologists (Mainly on
TV and Radio) want to indicate that
thunderstorms with light rain are expected,
they will call them Thundershowers, even
though there is no technical abbreviation
for a thundershower. It's just a good way
of taking the much stronger sounding word
"storm" out of the mix, and adding the
gentler sounding description of "shower".
Properly, thunderstorms have either no rain
(TS), light rain (TSRA-), moderate rain
(TSRA), or heavy rain (TSRA+). But, for a
viewer, it's tough to explain all that, so
we generally talk about weaker
thunderstorms as thundershowers, even
though there is "technically" no such
With this type of argument, TS and SH remain completely separate (eg. TSRA vs. SHRA). The + or - would be added to indicate intensity.